The thesis is concerned with the estimation of the sampled impulse-response of time-varying voiceband channels, and in particular with the proposed synchronous serial transmission of 16-level quadrature amplitude modulated digital data signals at 9600 bit/s over HF radio links. With such a system, the optimum detector at the receiver is a maximum likelihood detector implemented, for example, using the Viterbi algorithm. In this case, the detector requires knowledge of the sampled impulse-response of the channel. Channel estimators can also be used for estimating the response of any time-varying linear bandpass channel and need not be restricted in use only with a maximum likelihood detector. They may be employed in any such application where a time-varying channel must be tracked to ensure the correct operation of the detector. The thesis includes a description of the ionospheric propagation medium, with particular emphasis on the nature of the impairments that are likely to be encountered by the data signal. An appropriate model of the HF channel is simulated for subsequent use in testing the channel estimators. A summary is also given of the more important forms of channel estimators that are used for time-invariant or slowly time-varying channels. The characteristics of the HF radio medium may vary rapidly with time, so an estimator based on the Kalman filter is investigated in order to exploit the fast tracking capability of the filter. It is shown that inadequate modelling of the channel by the Kalman filter results in suboptimum performance (in the minimum mean square error sense) of the estimator, however, this can be improved by including a suitable predictor. The performance of the Kalman filter estimator, with and without the predictor, is then compared with the corresponding estimator which uses a feedforward transversal filter. The recently developed HF channel estimator based on the feedforward transversal-filter estimator is also investigated, but it is tested here over the simulated HF radio links with three independent Rayleigh fading sky waves, which represent typical poor conditions over actual links. Various degrees of prediction are also studied and based on the results, a change in the degree of prediction from that previously proposed is suggested as a better arrangement for use with the estimator when there are three sky waves. Finally, it is shown that a considerable reduction in the equipment complexity can be achieved by exploiting a selfcorrecting property of the estimator that has been discovered.